#2. Max./Min. on [-2,2]x[-1,1]

Quote:

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**dmbocci** 2.Find the absolute extremes of

Someone help me set this up?

Thanks

...

So for #2, I got critical points of (0,0) (0,1) (0,-1) (0,-2) (2,1) (2,0). But do I disregard (0,-1)&(0,-2) since they are outside my boundary?

Either way, the values I got are 0,4,6. So would 0 be my minimum and if so in my answer would I say that the function has absolute min. at both (0,1) and (0,0). Or would 4 be my min at (2,0)?

And 6 would be my abs. max. at (2,1)?

Does this look right?

How did you find the critical points?

The point (0, -1) is not outside your boundary. is a rectangular region with verticies (2,1), (2,-1), -2, -1), and (-2, 1).

#2. Max./Min. on [-2,2]x[-1,1]

Quote:

Originally Posted by

**dmbocci** 2.Find the absolute extremes of

Someone help me set this up?

Thanks

...

Quote:

Originally Posted by

**dmbocci** Not thinking on #2, whoops.

So idk if this is right, but now I have (-2,1)(-2,-1)(2,-1)(2,1)(-2,2)(2,-2)(1/2,-1)(-1/2,1) as my points to check. Does this look correct?

If so, my values output are 6,2,-1/2, and for (-2,2)&(2,-2)= 0 . But I would exclude those last two values?

Someone check my work?

How do we find the extrema for over some bounded closed region, Yes, look for critical points.

Critical points occur at locations within the interior of where and , or where these partial derivatives do not exist. They also occur along the boundary of , where directional derivatives along that boundary are zero, or don't exist. Take all of that into account, and find the minimum & maximum values of at all of the critical points.

. Setting this equal to zero gives: . . Setting this equal to zero gives: . This gives a critical point at the origin.

On the boundary : , so . So, is a critical point. Similarly, is also a critical point.

On the boundary : , so . So there are no critical points here, except at the end points.

Critical points are thus:

Evaluate at each of these points to find the extrema.